 Business
24 January, 04:43

A manager buys three shares of stock today, and then sells one of those shares each year for the next 3 years. His actions and the price history of the stock are summarized below. The stock pays no dividends.Time Price Action0 \$190 Buy 3 shares1 200 Sell 1 share2 200 Sell 1 share3 200 Sell 1 shareA. Calculate the time-weighted geometric average return on this "portfolio."B. Calculate the time-weighted arithmetic average return on this portfolio.C. Calculate the dollar-weighted average return on this portfolio.

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1. 24 January, 06:36
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a. The Geometric average return is 1.72%

b. The Arithmetic average return is 1.75%

c. The Dollar weighted average return is 2.61%

Explanation:

a) In order to calculate the time-weighted geometric average return we would have to calculate first the Holding period return as follows:

Holding period return = (200 - 190) / 190 = 5.263%

Hence, Geometric average return = (1 +.05263) ^ (1/3) - 1 = 1.72%

b) To calculate time-weighted arithmetic average return we have to make the following calculation:

Arithmetic average return = 5.263% / 3 = 1.75%

c) To calculate time-weighted arithmetic average return we would have to make the following calculation:

Dollar weighted average return=-190*3 + 200 / (1+r) + 200 / (1+r) ^2 + 200 / (1+r) ^3 = 0

= 2.61%